Pellegrini, 64, has signed a three-year deal at the London Stadium.
The former Manchester City and Real Madrid manager left his job with Hebei China Fortune over the weekend and succeeds David Moyes.
“Manuel brings a reputation for attacking football and getting the best out of his players,” said Sullivan.
“We believe he will attract new talent to the London Stadium as well as improving the current squad.
“Above all, he is a winner, who knows what it takes to succeed at the highest level and is driven to continue that success. Manuel is the first West Ham United manager to have a Premier League title on his CV, and we believe that his experience, quality and proven record of taking teams forward quickly will ensure that he is successful here.”
Chilean Pellegrini, who had been a priority target from the start of West Ham’s search for a new manager, will be joined at London Stadium by assistant Ruben Cousillas.
He replaces former Everton and Manchester United manager Moyes, who was appointed West Ham boss in November 2017 but released at the end of his contract after guiding West Ham to 13th place.
West Ham had explored the possibility of hiring Newcastle United manager Rafael Benitez, however they quickly concluded it would be hugely difficult for the Spaniard to leave St James’ Park.
Pellegrini, who was on a huge contract in China, has agreed to take a pay cut but it is anticipated he will become the highest paid manager in West Ham’s history.
Sullivan had previously said he intended to hire someone who had experience at the highest level.
He will hope Pellegrini, who won the 2013-14 Premier League title and two EFL Cups during his three years at Manchester City, in addition to qualifying the club for the Champions League semi-finals for the only time in their history, can bring some stability to West Ham.
The club have experienced huge problems during their first two seasons after leaving their legendary home at Upton Park.
They won just seven home Premier League games this season, a campaign which was marred by crowd trouble at London Stadium.
Five fans were banned for life by the club for running on to the pitch during their home fixture with Burnley on 10 March.
Other fans were also banned for life for throwing coins or objects “with intent to injure or harm”.
|Manuel Pellegrini’s Premier League record|
|Club||Season||Win %||Points per game|